You can use find for this. You use the folder above the folder1, folder 2 etc and execute these commands there.
find /folder/ -type f -name "*.jpg" -exec cp {} "jpgfiles/" +
find /folder/ -type f -name "*.mov" -exec cp {} "movfiles/" +
/folder/
is the parent folder here. you need to modify it to your parent folder.
EDIT: Thanks to @godlygeek for pointing it out. If you'd like to copy only unique files, you can use the below
find /folder/ -type f -name "*.jpg" -exec bash -c 'test ! -f jpgfiles/${0##*/} && { cp $0 jpgfiles/${0##*/}; }' {} +
find /folder/ -type f -name "*.mov" -exec bash -c 'test ! -f movfiles/${0##*/} && { cp $0 movfiles/${0##*/}; }' {} +
To copy the conflicting files with a unique file suffix:
find /folder/ -type f -name "*.jpg" -exec bash -c 'test -f jpgfiles/${0##*/} && { cp $0 jpgfiles/${0##*/}.$RANDOM; }' {} +
find /folder/ -type f -name "*.mov" -exec bash -c 'test -f movfiles/${0##*/} && { cp $0 movfiles/${0##*/}.$RANDOM; }' {} +
cp */*.jpg jpgfiles/ ; cp */*.mov movfiles/
)